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By R. Duncan, E. Drew

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1). 7) and the relation between the coordinate systems (x, y) and (ξ , η ) is given by the linear transformation Eξ = Ex cos ψ + Ey sin ψ , Eη = −Ex sin ψ + Ey cos ψ . Fig. 7). 9) and Eb (sin τ cos δ + cos τ sin δ ) = −E1 (cos τ cos δ1 − sin τ sin δ1 ) sin ψ + E2 (cos τ cos δ2 − sin τ sin δ2 ) cos ψ . e. also for τ = 0 and τ = π2 , resulting in Ea cos δ = E1 cos δ1 cos ψ + E2 cos δ2 sin ψ , −Ea sin δ = −E1 sin δ1 cos ψ − E2 sin δ2 sin ψ , Eb cos δ = E1 sin δ1 sin ψ − E2 sin δ2 cos ψ , Eb sin δ = −E1 cos δ1 sin ψ + E2 cos δ2 cos ψ .

58) This is strictly true if the angular frequency is a linear function of k. If ω (k) is more general, the group velocity depends on wave number, and the form of the wave packet (made up of waves with a finite range of wave numbers) will be distorted in time. That is, the pulse will disperse. 58), is larger depends on the properties of the medium in which the wave propagates. 52) as ω = kv, one finds dv dω = vg = v + k . 60) we see that normal dispersion dn/ dλ < 0 in the medium corresponds to dv/ dk < 0 .

This model was first given by Drude (1900) to explain the propagation of ultraviolet light in a transparent medium, but this model was later applied to the propagation of transverse electromagnetic radio waves in a tenuous plasma. 71) me v˙ = me r¨ = −e E0 e− i ω t with the solution v= e e E0 e− i ω t = − i E. 72) describes the motion of the electrons. Moving electrons, however, carry a current, whose density is J = − ∑ evα = −Nev = i α Ne2 E = σE. 73) This expression explains why the ions can be neglected in this investigation.

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